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6.9 Determining the Efficiency of Auxiliary Unitsin Passenger Cars

Michael Lindemann

Abstract

Both improvement of mechanical design and optimization of operating strategy ofaccessories provide a high potential for raising efficiency of modern vehicle drives. Itis necessary to have knowledge about the efficiency of all auxiliaries and the distribu-tion of the operating points of the components to achieve the best fuel economy im-

provement potential. Thus, there is a reasonable need for determining the efficien-cies of the accessories already integrated in the vehicle system.Starting with a description of an exemplary auxiliary system a model is introduced toemphasize the interaction between the single components and to describe them withcorresponding efficiency maps. These efficiency maps are represented by a polyno-mial approach. Ideally all input and output signals of all components should bemeasured to determine the unknown parameters of the polynomials. This yields to anunacceptable effort regarding measurement issues. Thus it will be shown which al-ternative signals can be captured and how these signals can help to determine theunknown polynomials, i.e. efficiency maps.It will be stated out how a suitable estimation of efficiency maps of an auxiliary sys-

tem in conventional vehicles can be achieved using a highly cost-efficient system ofmeasurement devices.

Kurzfassung

Die Optimierung von Nebenaggregaten bietet ein groes Potenzial zur Effizienzstei-gerung moderner Antriebssysteme in Pkws. Um die daraus resultierenden Ver-brauchsvorteile voll ausschpfen zu knnen, ist die Kenntnis der Wirkungsgrade allerEinzelkomponenten in ihren Betriebspunkten zwingend erforderlich. Aufgabe ist es

also, die Nebenaggregate whrend des Betriebs eines Fahrzeugs zu vermessen.Das Nebenaggregatesystem wird als Modell formuliert, das die Wirkungsbeziehun-gen zwischen den einzelnen Komponenten aufzeigt und ber Wirkungsgradkennfel-der miteinander verknpft. Die Kennfelder werden ber Polynomanstze definiert. ImIdealfall mssen zur Ermittlung der Kennfelder smtliche Ein- und Ausgangsgrender Komponenten gemessen werden. Der messtechnische Aufwand ist jedoch be-trchtlich. Es wird deswegen gezeigt, wie die Schtzung der unbekannten Parameterder Polynome, d.h. der Wirkungsgradkennfelder, aus der Erfassung anderer, abermglichst leicht zugnglicher Messgren erfolgen kann.Ergebnis dieser Untersuchung ist die Aussage, welche Messtechnik im Fahrzeugverbaut werden muss, um bei minimalen Kosten eine bestmgliche Abschtzung der

Effizienz eines Nebenaggregatetriebs zu erhalten.


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1. Introduction

Auxiliaries in passenger cars play an essential role in the overall fuel consumption ofa conventional vehicle. Appx. 8 % of the power contributed by the combustion engineis used to supply the auxiliary system [2], [4]. Thus, there is a need to improve both

the efficiency of the components and their operating point areas. To optimize thecomponents according to their technical design and to apply them in electric or hybridelectric vehicles it is indispensible to have knowledge about the efficiency of eachcomponent. The efficiency can be expressed in form of efficiency maps. Consideringseries vehicles it is rather impossible to find reliable information about the efficiencyof the auxiliary components. Thus the question does arise how the efficiency maps ofthe most important auxiliary components can be determined directly in the vehicle.Basically the input and output signals of the units can be measured to determine theefficiency. Calculating the input and output power of the components the ratio wouldyield directly to the efficiency. For instance measuring torque and speed of eachcomponent would lead to the mechanical input power. Mass flow, flow rate, and

pressure measurements are necessary to determine the output power ratings of theunits. However, this would lead to an unsuitable effort to equip the entire auxiliarysystem with all the mentioned measurement devices. To reduce this effort drastically,alternative signals have to be captured which are more easy to access like speeds,electrical quantities, or temperatures.This paper states out which measurement configuration has to be used to provide asufficient quality for determining the efficiency maps of the auxiliary components. Forthis purpose the efficiency maps are modeled with multi-dimensional polynomials.Basing on an exemplary accessory system a simulation model is introduced that con-tains the unknown parameters of the polynomials. Using further model assumptionsthese parameters are estimated with the acquired signals.

2. The Auxiliary System

Fig. 1 exemplary shows a typical auxiliary system. A belt drive is used to transmit thepower from the crankshaft of the combustion engine to the water pump, the steeringpump, the alternator, and the switchable a/c compressor. The ratios between thecomponents and the crankshaft are defined by the diameters of the correspondingpulleys. Usually, the ratios are constant. The torque from the combustion enginesplits into one part for the power train and another part for the auxiliary system. The

torque applied to each component itself depends on the requests of the correspond-ing components. Not the entire power is used by the auxiliary components. A certainpart is also used to perform friction and deformation work.The input power required from the auxiliary units is associated with the output powerthrough a certain efficiency. The efficiency depends on different influencing quanti-ties. Primarily it is the operating point given by the component speed and load. Fur-ther dependencies (e.g. from temperature) are present but will be neglected in thefollowing. Thus, the efficiencies can be represented as efficiency curves or efficiencymaps.


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Fig. 1: Typical Alignment of a Belt-Driven Accessory System

The efficiencies of the components are strongly dependent from many different influ-encing quantities. Thus, the efficiencies are defined over those quantities that arequite present during typical driving or operating scenarios (Table 1). These are speedand pressure for the water pump, for the alternator the current applied to battery andvehicle electric system, and for the a/c compressor the required cooling power of therefrigerant medium. The load dependency of the steering pump is neglected here, asthis load only appears during steering angle gradients and thus dependency of theefficiency of the steering pump is assumed to be dominated by the steering pumpspeed.

Table 1: Defined Influencing Quantities to Auxiliary Component Efficiency

Component Quantity 1 Quantity 2Water Pump Component Speed Coolant PressureAlternator Component Speed Electric CurrentStearin Pump Component SpeedA/C Compressor Flow Rate Compression Pressure

The model of the auxiliary system exemplary takes the defined quantities into con-sideration. However, a formal extension to other components can simply be realized.

The operating principle of the accessory system is explained with power dependen-cies between the components (Fig. 2).


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Fig. 2: Power Dependencies in the Accessory System

PAUX,indesignates the mechanical power required from the auxiliary components andprovided as the input power. This power is split into partial input power flows for thealternator, a/c compressor, water pump, and steering pump. Multiplying these inputpower ratings with the corresponding efficiencies leads to the output power signals ofthe auxiliary components.The task is to determine even these efficiencies of the components. The fundamentaldifficulty is that neither the input power ratings PA,in, PAC,in, PSP,in and PWP,in are

known, nor that the output power ratings PAC,out, PSP,outund PWP,outcan be measured.

3. Determining the Efficiency Maps

According to Fig. 2 the mechanical power of the auxiliary system input is the sum ofall partial input power ratings of the components. Thus PAUX,incan be written as

.,,,,, inWPinSPinACinAinAUX PPPPP (1)

The input power values of the components are associated with the output power val-ues through the efficiency maps. In general PAUX,inresults by

.,,,,

,

WP

outWP

SP

outSP

AC

outAC

A

outA

inAUX

PPPPP

(2)

Substituting the reciprocal efficiencies 1/ by eq. 2 can be written as

.,,,,, outWPWPoutSPSPoutACACoutAAinAUX PPPPP (3)


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To simplify matters eq. 3 is formulated in a more general way: PAUX,inis the sum of Rpartial power ratings, i.e.

.1

,,

R

r

outrrinAUX PP (4)

The reciprocal efficiencies now will be defined as one- or two-dimensional polynomi-als of order 2. For the one-dimensional case ris

.2

0

,

P

n

n

rnrr xa (5)

Using a two-dimensional polynomial, rcan be expressed as

.

2

0 0

,

P

k

k

j

jk

rjrnrr

p

p

pyxa (6)

ar,n is the nth polynomial coefficient of the rth reciprocal efficiency map. A one-

dimensional polynomial of order 2 defined by eq. 5 has 3, a two-dimensional polyno-mial given with eq. 6 has 6 coefficients. For a two-dimensional polynomial n runsfrom 0 to 5 and can be gained from the counter variables of the sums in eq. 6 by

.2

)1(j

kkn

pp

(7)

Regardless of which polynomial dimension is used for the reciprocal efficiencies, to-gether with eq. 5 or 6 eq. 4 can be represented as

,1

,,,

R

r

ir

P

i

irinAUX WpP (8)

whereas pr,iis the ithpolynomial coefficient of the rthcomponent, and Wr,idesignates

the product of the output power of the rth component with the ith polynomial varia-ble(s).Assuming in a first approach that all output power ratings can be measured and thusare known, and further assuming that all input signals of the efficiency map can becaptured, the unknown polynomial coefficients can be determined using a leastsquares approach.For applying the least squares approach the measurement values of the input powersignals of the auxiliary components have to be modeled with eq. 8. The unknownpolynomial coefficients can then be determined minimizing the least squares errorgiven by

,)(1

2

1

,,,

N

k

R

r

ir

P

i

irinAUX WpkP (9)

solving the matrix equation


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.1ZWWP (10)

Pis the vector with the polynomial coefficients

],...,,,[ 21T

R

TTpppP (11)

Wis a square matrix which results from the W-terms in eq. 8 to

.

2

10

1110

101011

2

10

RPRP

RP

WWW

WW

WWWWW

W (12)

ZWis a matrix combining the terms W r,iwith the PAUX,in measurement values by theexpression

.,11,10,

T

RPinAUXinAUXinAUX WPWPWP ZW (13)

Hence, to determine the unknown polynomial coefficients of the reciprocal efficiencymaps, eq. 10 has to be solved. Before the number R of the considered auxiliarycomponents has to be selected. Furthermore is has to be defined if the efficienciesdepend on one or two influencing quantities. The polynomial of the corresponding

component has two be defined using a one- or two-dimensional approach according-ly. To solve eq. 10 the minimum number of measurement values results from thenumber of coefficients being used to model the reciprocal efficiencies.For each set of measurement data the input power PAUX,inas well as the output pow-er ratings of the auxiliary components and the values of the influencing quantities hasto be given. Using these data the matrices in eq. 12 and 13 can be built up and con-sequently eq. 10 can be solved. The efficiency maps then can be obtained as re-ciprocals of the reciprocal efficiencies .

4. Strategy for Measuring the Efficiency MapsSolving eq. 10 (assuming that the output power ratings of the auxiliary componentsare known) all efficiency maps can be gained at once. However, for the defined sys-tem of equations both the input power ratings of the components and the efficiencymaps itselves are unknown. Thus solving eq. 10 leads to a reasonable solution in amathematical sense. But in a physical sense the results are not feasible as one ob-tains negative efficiencies or efficiencies > 1. To solve this problem either the systemof equations has to be extended in a reasonable way or has to be restricted appro-priately. Another way is to choose a suitable measuring approach to determine theefficiencies subsequently.

The basic concept is to apply reasonable operating configurations in that way thatonly one component burdens the combustion engine whereas the other components


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are deactivated anyhow. This procedure is summarized in the table below and will beexplained in the following.

Table 2: Approach for Subsequent Determination of the Efficiencies of AuxiliaryComponents

Step Measure Means Result1 Deactivating Alternator Full Battery, Switching off

Electric LoadsSpeed and Load De-pendent EfficiencyMap of Cooling andSteering Pump

Deactivating A/CCompressor

Switching off Air Condi-tion

Minimize Power of

Steering Pump

Driving w/o Steering

2 Charging Alternator Switching on ElectricLoads

Efficiency Map of Al-ternator

3 Activating A/C Com-pressor

Cooling Vehicle Cabin Efficiency Map of A/CCompressor

Concerning the a/c compressor and the alternator it is a quite simple task to deacti-

vate the mentioned components (switching off the climate control and operating theelectric vehicle system with heavily reduced loads and a full battery). However, thecooling pump and the steering pump are running continuously with a certain load:The cooling circuit of the engine is activated immediately after engine start. Thesame holds for the hydraulic steering support. Both the pressure and the speed de-pendent flow rate of the coolant lead to permanent power losses within the auxiliarysystem. And even the steering support is active after engine start. The steering pumpalready runs and provides a pressure with a flow rate even if no steering angle ispresent. This leads to additional mechanical losses.Thus in a first step the efficiencies of the steering pump and the coolant system haveto be determined. As the input power ratings of the cooling pump and the steeringpump cannot be measured separately, it is not possible to calculate the efficiency ofthese components independently. Therefore both components have to be consideredas one consumer. For measuring the total efficiency of steering and water pump thealternator has to be deactivated. This can be realized running the vehicle electric sys-tem with a fully charged battery and just applying the minimum number of electricconsumers. Furthermore the a/c compressor has to be switched off.Operating the vehicle for measuring purposes it has to be taken into considerationthat all driving scenarios are realized without steering angle at different enginespeeds. Operating the vehicle beginning from a cold start, different coolant tempera-tures result what leads to different pressures within the coolant liquid. Measuring the

pressure of the coolant liquid as well as the component speeds, a speed and loaddependent efficiency map can be obtained.


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For the second step the driving scenarios are repeated with activated alternator, i.e.operating the vehicle electric system with different currents. The difference betweenthe measured input power PAUX,inof the auxiliary system and the input power of thecooling and steering pump calculated backwards with the output power ratings and

the efficiency map is determined. This difference then equals the input power of thealternator. As the input and output power of the alternator is known, the efficiencymap can be estimated directly. In this way the efficiency of the a/c compressor is de-termined applying different pressures to the refrigerant medium by choosing differentset temperatures of the vehicles cabin.

5. Results

The strategy to identify the efficiencies of the auxiliary components described in theformer chapter is verified using a simulation model with a 237 Nm/80 kW diesel en-

gine together with the accessory components specified in table 3. Only for verificationpurposes it is further assumed that the output power ratings of the components areavailable.

Table 3: Specification of the Auxiliary Components Used in the Simulation Model

Component ParameterCooling Pump Ratio 1.2

Max. Flow Rate 100 l/min.Nominal Pressure 1.2 bar

Alternator Ratio 2.7Max. Power 1,8 kW@12 VSteering Pump Ratio 1.2

Max. Flow Rate 100 l/min.Nominal Pressure w/o Steering Angle 6 bar

A/C Compressor Ratio 1.5Max. Flow Rate 25 l/min.Pressure Range 3 to 20 bar

The corresponding efficiency maps of the components are shown in the following Fig.3 and 4.Beside the efficiency contour lines the bold dots symbolize the operating points ap-plied to the auxiliary system to identify the efficiencies. The number of measurementpoints depends on the order of the polynomials that describe the reciprocal efficien-cies (see eq. 5 and 6). As for all polynomials an order of two has been chosen, atleast 3 or 6 measurement values per line or map have to be acquired. Furthermorethe operating points should be inside a typical operating range to avoid focusing onunusual operating areas. Abnormal loads thus should be avoided.


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Fig. 3: Efficiency Map of Cooling Pump (left) and Efficiency Line of Steering Pump(right)

Fig. 4: Efficiency Maps of A/C Compressor (left) and Alternator (right)

As described in table 2 the first step of the identification strategy is to determine thecommon efficiency map from cooling and steering pump. Using the parameterizationabove, simulation runs are accomplished to acquire the output power of the compo-nents for given speeds and coolant pressures.The total efficiency of cooling and steering pump can now be obtained using eq. 10.The result is given in Fig. 5 (right). The left plot shows the input power of the auxiliary

system and the output power ratings of the cooling and steering pump. As expected,an averaged efficiency map results combining both the efficiency map of the waterpump and the efficiency line of the steering pump (Fig. 3). As the efficiency map usedas a cooling pump parameter does not vary strongly within the range applied in thesimulation (1.1 to 1.3 bar), almost vertical contour lines result in Fig. 5 (right). Itshould be stated out here, that for measurements at real auxiliary systems furtherloads appear which are not covered by the steering and water pump, such like de-formation of the belt, turbulences, belt friction, and so on. Thus, the calculated effi-ciency in general is less than the real efficiency of both components.


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Fig. 5: Measured Power at Auxiliary System (left) and Estimated Common EfficiencyMap from Water and Steering Pump (right)

According to table 2, for the second step the alternator will be activated. Using thecommon efficiency map of water and steering pump the input power of both compo-nents can be determined. Subtracting this power from the input power of the auxiliarysystem leads to an estimation of input power of the alternator. The alternator efficien-cy map then can be determined using eq. 10.Fig. 6 (left) again shows the input power of the auxiliary system. The saw toothshaped line is due to increasing load of the alternator. The input power of cooling andsteering pump calculated backwards from the output power ratings is shown as adashed line. The difference of both lines equals the mechanical alternator input pow-er. The resulting efficiency map is illustrated in Fig. 6 (right) and basically matches

the real efficiency map used in the simulation. Deviations can be observed in thegradient of the efficiency contour lines with increasing speed. This is due to the loworder of the polynomial model of the reciprocal efficiency map.

Fig. 6: Measured Power at Auxiliary System (left) and Estimated Efficiency Map fromAlternator (right)

As accomplished with the alternator the same strategy is applied now to the a/c com-pressor. Different compressor power settings are requested defining different cooling

temperatures for the vehicle passenger cabin with activated air condition. This leadsto different pressures of the refrigerant liquid. Again making use of the efficiency


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maps determined in the foregoing steps the input power ratings of alternator, cooling,and steering pump can be estimated backwards. The difference with the auxiliaryinput power again leads to the mechanical a/c compressor input power. The resultingefficiency and the power distributions are shown in Fig. 7.

Fig. 7: Measured Power at Auxiliary System (left) and Estimated Efficiency Map fromA/C Compressor (right)

Again the estimated efficiency map basically matches the parameterized efficiencymap of the a/c compressor. Deviations can be observed around the maximum area.As the estimated efficiency is too high, the consequence is that backwards calculatedpower of the other components is lower than actually have been. This leads to a 5percentage point higher efficiency value. As already emphasized for the alternatorthe gradient of the contour lines is lower than it is for the real map. This again is due

to the low order of the polynomial for modeling the reciprocal efficiency map.

6. Optimized Measurements

The last chapter pointed out which identification quality can be expected for the effi-ciency maps if all output power ratings of the considered components can be ob-tained. Increasing the order of the polynomials of the reciprocal efficiency maps mayprovide better results, but basically a polynomial of order 2 is sufficient to achieve asuitable estimation. This statement even holds if the considered operating ranges are

not extended to the absolute component limits.As already mentioned at the beginning, practically it is quite impossible to measureall output power ratings of the auxiliary components due to cost and safety reasons.Thus, different alternative signals are necessary to achieve suitable estimations ofthe component output power if the power signals cannot be measured directly. Pro-posals for the auxiliary components are given in the next sections.

6.1 Alternator

The output power of the alternator is the product between alternator current and volt-

age of the vehicle electric system. These signals are usually easy to access. Measur-


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ing the current, a clamp-on ammeter is required; the voltage of the vehicle electricsystem should be directly measured at the terminals of the alternator.

6.2 Water Pump

The output power of the water pump is the product between the difference pressureof the pump and the flow rate of the coolant. Basically neither flow rate nor coolantpressure are measured online in series vehicles and provided over the CAN bus.Thus, alternative signals are required.Increasing engine temperature and consequently rising temperature of the coolantleads to an expansion of the coolant liquid. This process is accompanied by an in-creasing of the coolant pressure. If the pressure exceeds a certain limit a valveopens and redirects a part of the coolant into the expansion tank. Below this limit thepressure increases almost linearly with the coolant temperature (law of Amontons).As the coolant temperature is a signal that usually is available in series vehicles, this

signal can be used to determine the coolant pressure.The flow rate of the coolant depends on the speed of the water pump. Due to the lawof similarity [5] it can be assumed that the flow rate and the pump speed are lineardependent to each other. Hence the power of the water pump can be calculated intypical operating ranges with

.1 000 WPWP napQpP (14)

p0 is the initial pressure of the coolant, 0is the volumetric coefficient of expansion,= 0describes the temperature difference compared to the initial temperature0, and a0contains the displacement volume of the pump.

6.3 Steering Pump

The output power of the steering pump is (as it is for the water pump) the productbetween the difference pressure of the pump and the flow rate of the hydraulic oil.As it holds for the water pump the flow rate again is proportional to the pump speed.Unlike the water pump, for the steering pump neither temperature not pressure in-formation can be achieved. Thus measuring the pressure directly at the high pres-sure side of the steering pump is indispensable. Together with the flow rate the out-put power of the steering pump can be estimated with

.0 SPSP napQpP (15)

p is the measured pressure of the hydraulic oil and a0 contains again informationabout the displacement volume of the pump.


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6.4 A/C Compressor

Just like the steering and water pump power, the a/c compressor power also can beobtained from the product between the pressure difference and the flow rate of therefrigerant medium.

For modern vehicles information about the pressure at the high pressure side of thecompressor usually is available. The pressure at the compressor input usually is notmeasured, but the temperature at the evaporator. The corresponding pressure canbe obtained from the steam table for the refrigerant medium. Furthermore it has to betaken into consideration that there is an averaged overheating of 6 K of the refriger-ant medium. Using the law of Amontons the pressure at the compressor input can beestimated. Thus, for the pressure difference between high and low pressure side ofthe a/c compressor one obtains

.1 0 Overinoutinout ppppp (16)

where p represents the pressure difference between output poutand input pin, p(in)is for the pressure gained from the steam table of the refrigerant medium measuredat temperature inat the evaporator, 0 is the volumetric coefficient of expansion ofthe refrigerant medium and overis for the overheating temperature level.The flow rate Q of the refrigerant medium through the compressor can be gained bythe equation

.geomQQ (17)

is the volumetric efficiency of the compressor. Besides other influence variables(e.g. temperature of the inflowing refrigerant) the volumetric efficiency strongly de-pends on the pressure ratio of the compressor. Qgeomis for flow rate that can be cal-culated by the geometrical data of the compressor, i.e. the volume Vgeom per timeunit. Assuming a controllable compressor the volume Vgeomusually can be controlledbetween 0 and Vgeom,maxusing a wobbling disk, e.g [1]. Thus Qgeomis directly propor-tional to the compressor speed so that the flow rate can be calculated as

,nsVQ geom (18)

where is the pressure ratio pout/pin, n represents the compressor speed, and s is thecontrollable stroke of the compressor piston. Neglecting pressure losses at the intakethe volumetric efficiency can be calculated to [3]

.1025,0111 162,01/1 c (19)

c is the clearance ratio and is the isentropic exponent of the refrigerant medium.


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6.5 Measurement System

Making use of the assumptions above the output power signals of the auxiliary unitscan be determined. The following Fig. 8 shows the corresponding measurement sig-nals that have to be captured at the auxiliary system.

Fig. 8: Points of Measurement to Determine the Input Power of the Auxiliary Unitsand the Component Output Power Ratings

For measuring the auxiliary system it is indispensable to have knowledge about theinput torque to the auxiliaries. Thus it is necessary to apply a torque sensor to theaccessory input. The acquisition of the alternator current should be realized with aclamp-on ammeter directly at one of the alternator output terminals. The hydrauliccircuit of the steering support has to be equipped with a pressure sensor at the out-put side of the pump. All other signals can be measured without any further instru-mentation directly from the power train or comfort CAN bus.In comparison to the direct measuring of all input and output power signals themeasurement system introduced in Fig. 8 is much simpler. The most cost-intensivecomponents are the torque adapter and the pressure sensor at the output of thesteering pump. A disadvantage is that the output power signals only can be obtainedwith a limited accuracy. Furthermore the efficiencies of the cooling and steeringpump including other additional losses cannot be determined separately.


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7. Summary

Determination of the efficiency of auxiliary units even integrated in a vehicle is anambitious task that could require highly cost-intensive efforts concerning the meas-urement equipment. This is due to the fact that all input and output power signals of

all components had to be acquired.Considering an exemplary auxiliary system with four different components a funda-mental set of equations was introduced to determine the efficiencies of all definedcomponents. For this set of equations both the efficiencies and the component inputpower ratings of the auxiliary units are unknown. Describing the reciprocal efficiencymaps as polynomials, it is possible to determine the unknown polynomial coefficientsmaking use of a subsequent activation of the accessories. A suitable quality of theestimated maps could be proven using a simulation approach for verification purpos-es. However, knowledge about the output power ratings of the units is required. Itwas further shown how these power ratings can be obtained with easy accessiblesignals.

Using this approach it is possible to achieve information about the efficiencies of theconsidered accessory units without using sophisticated measurement devices.

List of References

[1] Matthies, H. J.; Renius, K. T.: Einfhrung in die lhydraulik, 6. Auflage, Vieweg+ Teubner Verlag, Wiesbaden, 2008

[2] Lunanova, M.: Optimierung von Nebenaggregaten: Manahmen zur Senkung

der CO2-Emission von Kraftfahrzeugen, Vieweg + Teubner Verlag, Wiesbaden,2009

[3] Cikonkov, R.; Hilliweg, A.: Kolbenverdichter Simulation des Leistungsverhal-tens beim Einsatz in einem Verflssigungssatz, KI Luft- und Kltetechnik,3/2003

[4] Rumbolz, Ph.; Piegsa, A.; Reuss, H.-Ch.: Messung der Fahrzeug-internen Leis-tungsflsse und der diese beeinflussenden Gren im real-life Fahrbetrieb, 7.VDI Tagung Innovative Fahrzeugantriebe, Dresden, 2010

[5] Surek, D.; Stempin, S.: Angewandte Strmungsmechanik fr Praxis und Stu-dium, 1. Auflage, B. G. Teubner Verlag, Wiesbaden, 2007

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